Answer

Solution

UPSC Prelims

CSAT Year Wise (Temporary Link, This will be removed and no PDFs shall be downloaded here. Please download CSAT subject wise files) / सी सैट

Theme:

CSAT 2023

Q20 2023, CSAT 2023

A, B, C working independently can do a piece of work in 8, 16 and 12 days respectively. A alone works on Monday, B alone works on Tuesday, C alone works on Wednesday; A alone, again works on Thursday and so on. Consider the following statements:
1. The work will be finished on Thursday.
2. The work will be finished in 10 days.
Which of the above statements is/are correct?

A, B, C अलग-अलग काम करते हुए किसी काम को क्रमश: 8, 16 और 12 दिनों में पूरा कर सकते हैं। अकेला A सोमवार को काम करता है, अकेला B मंगलवार को काम करता है, अकेला C बुधवार को काम करता है; A फिर से अकेला बृहस्पतिवार को काम करता है और इसी तरह यह क्रम जारी रहता है। निम्नलिखित कथनों पर विचार कीजिए:
1. यह काम बृहस्पतिवार को पूरा हो जाएगा।
2. यह काम 10 दिनों में पूरा हो जाएगा।
उपर्युक्त कथनों में से कौन-सा/से सही है/हैं?

Explanation Please wait..

Let's analyze the situation based on the given information:

A completes the work in 8 days, B in 16 days, and C in 12 days.

They work on alternate days starting from Monday.

To determine when the work will be finished and if it will be finished in 10 days, we need to calculate the work done by each person on each day.

Approach:

A, B, and C can complete a task in 8, 16, and 12 days respectively if they work independently.

A completes 1/8th of the work in one day. B completes 1/16th of the work in one day. C completes 1/12th of the work in one day.

We can do the question considering the total work as the least common multiple (LCM) of 8, 16, and 12, which is 48 units.

So, Efficiency of A = 48/8 = 6 units/day

Efficiency of B = 48/16 = 3 units/day

Efficiency of C = 48/12 = 4 units/day

Calculations:

The total work completed in 3 days (Monday, Tuesday, Wednesday) = 6 + 3 + 4 = 13 units.

The work completed in the next 3 days (Thursday, Friday, Saturday) = 6 + 3 + 4 = 13 units.

The work completed in the next 3 days (Sunday, Monday, Tuesday) = 6 + 3 + 4 = 13 units.

Total work in 9 days = 39 units => 48 – 39 = 9 units work is still remaining.

Now if only A and B works for next 2 days => 6 + 3 = 9 units.

Hence, the work will be completed in the next 2 days (Wednesday, Thursday).

Therefore, the total work completed in 11 days is 48 units, and the work will be finished on Thursday.

This means that Statement 1 is correct, but Statement 2 is incorrect.

Therefore, option (a) is the correct answer.

Let's analyze the situation based
on the given information:

<ul><li> 
A
completes the work in 8 days, B in 16 days, and C in 12 days.</li></ul>

<ul><li> 
They
work on alternate days starting from Monday.</li></ul>

To
determine when the work will be finished and if it will be finished in 10 days,
we need to calculate the work done by each person on each day.

Approach:

<ul><li> 
A,
B, and C can complete a task in 8, 16, and 12 days respectively if they work
independently.</li></ul>

<ul><li> 
A completes 1/8th of the work in one day. B completes
1/16th of the work in one day. C completes 1/12th of the work in one day.</li></ul>

<ul><li> 
We
can do the question considering the total work as the least common multiple
(LCM) of 8, 16, and 12, which is 48 units.</li></ul>

<ul><li> 
So,
Efficiency of A = 48/8 = 6 units/day</li></ul>

<ul><li> 
Efficiency
of B = 48/16 = 3 units/day</li></ul>

<ul><li> 
Efficiency
of C = 48/12 = 4 units/day</li></ul>

Calculations:

<ul><li> 
The
total work completed in 3 days (Monday, Tuesday, Wednesday) = 6 + 3 + 4 = 13
units.</li></ul>

<ul><li> 
The
work completed in the next 3 days (Thursday, Friday, Saturday) = 6 + 3 + 4 = 13
units.</li></ul>

<ul><li> 
The
work completed in the next 3 days (Sunday, Monday, Tuesday) = 6 + 3 + 4 = 13
units.</li></ul>

<ul><li> 
Total
work in 9 days = 39 units => 48 – 39 = 9 units work is still remaining.</li></ul>

<ul><li> 
Now
if only A and B works for next 2 days => 6 + 3 = 9 units.</li></ul>

<ul><li> 
Hence,
the work will be completed in the next 2 days (Wednesday, Thursday).</li></ul>

<ul><li> 
Therefore,
the total work completed in 11 days is 48 units, and the work will be finished
on Thursday.</li></ul>

<ul><li> 
This
means that Statement 1 is correct, but Statement 2 is incorrect.</li></ul>

<ul><li> 
Therefore,
option (a) is the correct answer.</li></ul>

CSAT Year Wise (Temporary Link, This will be removed and no PDFs shall be downloaded here. Please download CSAT subject wise files) / सी सैट

Q20 2023, CSAT 2023

Explanation Please wait..

व्याख्या Please wait..

Quick Links

John Doe

CSAT Year Wise (Temporary Link, This will be removed and no PDFs shall be downloaded here. Please download CSAT subject wise files) / सी सैट

Q20 2023, CSAT 2023

Explanation Please wait..

व्याख्या Please wait..

Quick Links

Question Meta

Ancient History / प्राचीन इतिहास

John Doe